ILĀ : daughter of Vaivasvata manu.

1) genealogy.

descended from Viṣṇu in this order:– Brahmā–Marīci–Kaśyapa–Vaivasvata manu–Ilā. Vaivasvata manu was the son of Kaśyapa by his wife aditi, and Ilā the daughter of Vaivasvata manu by his wife, Śraddhā. Ikṣvāku, the ancestral father of the solar dynasty of Kings was brother of Ilā.

2) Vaivasvata manu and Śraddhā had, for a long time no children. manu got performed once by agastya a yajña to propitiate the Mitrāvaruṇas so that a son might be born to him (manu). soon a daughter was born to him and she was called Ilā. then manu asked Vasiṣtha why a daughter was born to him instead of a son for whom the yajña was performed by agastya. At once, Vasiṣtha by his will-power turned the girl Ilā into a boy, and the boy was named Sudyumna. [Bhāgavata] .

3) Sudyumna again turned into woman.

once Śunaka and some other sages went to the great forest Kumāra Vana near Kailāsa to salute Sri Parameśvara ignorant of the fact that just then Pārvatī and Parmeśvara were enjoying themselves. The sudden appearance of Śunaka and others was not relished by the divine couple, who were then naked. they therefore, pronounced the curse that anybody who entered the forest in future would be turned into a woman. [Bhāgavata] . Sudyumna, now a young man, went for hunting one day. Sudyumna who was ignorant of this curse entered this forest with his friends while hunting. At once all of them were transformed into women. grief-stricken, they stayed in the forest for some days, and then started for the palace. Sudyumna bearing the name Ilā walked at the head of the party as a beautiful woman. On the way Budha met Ilā, they fell in love with each other and got married. A son, Purūravas was born to Budha by Ilā. [Bhāgavata] .

4) transformation again;

Ilā expressed to Vasiṣṭha, her grief at having been turned into a woman, the sage requested Śrī Parameśvara to restore her to her former form as a man. Śiva said that Ilā would be a man and a woman every alternate month, throughout life. during the month when she was a man he would engage himself in matters of government, and the next month, when a woman, she would stay in the inner apartments in the palace. Brahmāṇḍa Purāṇa, chapter 32 says that Ikṣvāku, brother of Purūravas ruled the state till the latter became a major. As soon as Purūravas attained majority Sudyumna handed over to him the reins of government and retired to the forest for tapas, and during this period he was taught the Navākṣara mantra by sage Nārada. Sudyumna adored Devī with this mantra. she appeared to him and blessed him with the state of salvation. [Bhāgavata] . Purūravas married Urvaśī, and ruled the country. [Bhāgavata, 9th Skandha] ;[Devī Bhāgavata, First Skandha] ;[M.B. Ādi Parva, Chapter 75] ;[Anuśāsana Parva, Chapter 147, Verse 26] .
ILĀ II A river. At the birth of Subrahmaṇya this river paid homage to him with fruits and roots. [M.B. Anuśāsana Parva, Chapter 86, Verse 24] . Dharmaputra along with the brahmins bathed in this river. [M.B. Vana Parva, Chapter 156, Verse 8] .

See this

Characters Of Yaduvansh